According to Wikipedia (https://en.m.wikipedia.org/wiki/Chimor)
According to legend, its capital of Chan Chan was founded by Taycanamo, who arrived in the area by sea.
I was really intrigued by this so I thought I’d take a look.
The Wikipedia article doesn’t say that the first king of Chimor came from the west, just that he came by sea.
Page 783 of the ‘Handbook of South American Archaeology’ contains a short account of these origins:
A foreign noble named Taycanamo arrived in the Moche Valley, disembarking from a balsa log raft like those from far northern Peru and claiming to be sent by a great lord, from across the sea.
The authors cite ‘Rowe 1948: 28-30’, which is the book ‘The Kingdom of the Chimor’ by J.H. Rowe, which also contains a similar passage, translated from a 1604 writing titled ‘An Anonymous History of Trujillo’:
It is not known whence came this… except that he gave them to understand that a great lord… had sent him to govern this land… from across the sea. The yellow powders which he used in his ceremonies and the cotton cloths which he wore to cover his shameful parts are well known in these lands and the balsa of logs is used on the coast of Payta and Tumbez from which it is presumed that this Indian did not come from a very distant region.
As you can see, it seems that Taycamo came by sea from somewhere in northern Peru, close to the lands of the Chimor.
In fact, if we look at the map on page 29 of Rowe’s book, we can see that Payta and Tumbez (where Taycamo’s balsa of logs apparently looks like it came from) is not very far from the kingdom of Chimor, and Taycamo’s ceremonial and clothing style was apparently already familiar to these people.
Unfortunately neither of these sources elaborate on whether they think this account is historically accurate, but if it is true, then it appears that Taycamo traveled a comparatively short distance by sea, rather than coming from the west.
Bibliography:
Moore, J.D. and Carol, J.M. (2008). Handbook of South American Archaeology, p.738.